Model Predictive Control (herein referred to as “MPC”) is a technology utilized in various Advanced Process Control (herein referred to as “APC”) systems. MPC-based systems have been implemented on thousands of refining and chemical processes over the past two decades. DMCplus®, and the earlier version, DMC, (both available from Aspen Technology, Inc. of Cambridge, Mass.) is a widely used MPC-based system. In an MPC-based system, a model is used to predict the future behavior of a process, given the current and history input information (e.g., measurements of process conditions). An optimized control plan is calculated such that the predicted future response and the control action needed to achieve the response will satisfy certain predefined criteria. Once the calculated control plan is implemented (e.g., after the first point of the control move is implemented), the process measurements are collected and fed back to the controller to update the model predictions. A new control plan calculation is then initiated.
In an MPC-based controller, the model plays a central role. The model not only dictates the accuracy of the predictions, but it also affects the control actions. Model uncertainty is inevitable in practice, so the quality of the model should be evaluated based on its relevant application (i.e., not just the model's predictive ability, but also its control performance).
Collinearity in the model impacts control performance significantly. Excessive control action is one problem associated with unsolved collinearity in a model. The action of the controller, at least to some extent, mirrors the response from the model universe. When the model is nearly collinear, but is not perfectly collinear, excess control action may be generated in response to changes in system constraints or to achieve insignificant objective function improvements. A second problem associated with unsolved collinearity is that of unstable closed-loop control. If both the model and the underneath process are nearly collinear, but they have different directionality, the closed-loop system will become unstable. A third problem associated with unsolved collinearity is poor process performance. If the underlying process being modeled is not collinear, but the model is, then the controller will treat the process as if it has fewer degrees of freedom in the controlled variables and will not explore the full potential of the process. Poor control performance can even cause damage to the normal operation of the process.
Numerous attempts have been made to alleviate the problems posed by collinearity to MPC implementations. For example, some tools developed by the APC community detect a collinear model, or model subsets, through the use of either Relative Gain Array (herein referred to as RGA) or Singular Value Decomposition (herein referred to as SVD) to detect a collinear model or model subsets. See, for example, J. M. Maciejowski's “Multivariable Feedback Design,” published by Addison-Wesley Publishing Company, 1990, ISBN 0-201-18243-2, the entire teachings of which, are incorporated herein by reference. Some of those tools also adjust the model to minimize the RGA number; however, those approaches are limited to a 2×2 system.
A need exists for methods and articles for systematically detecting, verifying, and repairing collinear models.